arXiv subjects

Markus Reibnegger

Publications and source records attributed to Markus Reibnegger.

3 recordsLinked to original sources

arXiv2026

A Mixed Robinson--Schensted--Knuth Construction in the Representation Theory of $\mathrm{GL}_n$ over Local non-Archimedean Fields

We present a simple combinatorial method for computing the socle of representations of $\mathrm{GL}_n(F)$, where $F$ is a local non-Archimedean field, parabolically induced from two ladder representations. We adapt recent approaches to such problems using the classical Robinson--Schensted--Knuth correspondence (RSK) and introduce a new variant of RSK that we call mixed-RSK. Some combinatorial properties of this map are investigated and then used to resolve a conjecture of Erez Lapid.

math.CO↗

arXiv2026

A new antisymmetrizer-to-determinant formula and a conjecture of Colomo and Pronko

Identities asserting that an antisymmetrizer admits a determinantal expression are central to several proofs of counting formulas for alternating sign matrices. Antisymmetrizers appear also frequently in symmetric function theory as, for instance, the Hall-Littlewood polynomials can be realized via antisymmetrizers. In this paper, we establish a new identity of this type, thereby proving a conjecture of Lukas Riegler and one of the authors. We also elaborate on a related antisymmetrizer that may be pivotal in resolving a beautiful conjecture of Colomo and Pronko, and we formulate a version of their conjecture tailored to the suggested approach.

math.CO↗

arXiv2026

More minor summation formulae

We prove determinantal-Pfaffian formulae that simultaneously generalise the Pfaffian minor summation formula of Ishikawa and Wakayama and Byun's recent minor summation formula. These formulae are based on factorisation formulae for the determinant of the sum of a skew-symmetric matrix and a rank-1 matrix. Applications include a Cauchy-type identity for skew Schur functions.

math.CO↗